SOLUTION: The sum of the squares of two consecutive integers is 13. Find the integers and explain your steps as you solve.

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Question 20078: The sum of the squares of two consecutive integers is 13. Find the integers and explain your steps as you solve.

Answer by pwac(253) About Me  (Show Source):
You can put this solution on YOUR website!
let x= first number
so second is x+1
x%5E2+%2B%28x%2B1%29%5E2=13multiplying out bracket gives
x%5E2%2Bx%5E2%2B2x%2B1=13sum and rearrange
2x%5E2%2B2x-12=0divide through by 2
x%5E2%2Bx-6=0 a quadratic that factors
(x-2)(x+3)
x=2
x=-3
consecutive numbers are 2 and 3
the minus sign is irrelevant as -3 squared is same as 3 squared
Pete